Heat a large nonstick pan over high heat and add the oil. When the oil is hot, add the beef and sear, flipping after a minute or two until browned on both sides. Remove to a plate and set aside. Do not clean the pan.
Add the mushrooms and a pinch of salt. Cook, stirring occasionally until the mushrooms release their liquid and begin to brown, 5-10 minutes. Add the shallots and garlic and cook until the shallots are soft and translucent, about 3 minutes more. Add the white wine and cook until reduced by half, about 5 minutes. Add the chicken stock, gelatin, soy, sweetener, Worcestershire sauce, and thyme. Cook until reduced and thickened, 5-8 minutes more.
While the sauce reduces, cook the green beans. I like to microwave them for about 5-8 minutes, or until tender crisp. Alternatively, you can blanch them on the stovetop, see notes.
While the beans cook, combine the cottage cheese, garlic, lemon, zest, salt, and pepper in a blender. Blend until completely smooth, adding water as needed to obtain a thick, smooth sauce.
Toss the beans in the blended sauce (it is important that they are at room temperature and not hot or the cottage cheese sauce will curdle) and add the steak back to the pan of mushroom sauce to rewarm just before serving. Serve the beans alongside the steak.